CHAPTER 6 AN INTEGRATED APPROACH TO FINANCIAL ANALYSIS

CHAPTER 6

AN INTEGRATED APPROACH TO FINANCIAL ANALYSIS

TABLE OF CONTENTS

• INTRODUCTION

• NOMINAL, REAL PRICES AND INFLATION

• MARKET AND REAL EXCHANGE RATES

• INFLATION AND NOMINAL INTEREST RATE

• IMPACTS OF INFLATION

– 5.1 DIRECT IMPACTS

– 5.2 TAX IMPACTS

INTRODUCTION

• Projects which are feasible in the absence of inflation could turn out to be unfeasible with inflation.

• Countries have inflation at varying levels.• Inflation effects the outcome of the project through direct

impacts (on investments, A/R, A/P, cash held, interest expenses) and tax impacts (interest expenses deductions, depreciation expenses and inventories and cost of goods sold).

• In this chapter we will see how inflation effects the outcome of a project and how we could integrate it into our model in order to capture its effects.

2. NOMINAL, REAL PRICES AND INFLATIONS

1. Nominal Prices (Current prices)P1

t,P2t, P3

t……….. Pnt

2. Price Level PL

t = in (Pi

t Wi)

Where: i = Individual good or service included in the market basketPi

t = Price of the good or service i at a point in timeWi = Weight given to the price of a particular good or service (i); where wi = 1

Note: it is generally useful to express the price level of a basket of goods and services at a specific point in time in terms of a price index (P )

PtI = Pt

L/ PBL

Where PtL = Price level in period (t)

PBL = Price level for the base period (B)

2. NOMINAL, REAL PRICES AND INFLATIONS (Cont’d)

3. Changes in Price Level (Inflation)

• Measured in terms of a price index:

gP = ((PIt - PI

t-1 )/(PIt-1 )) * 100

4. Real PricesPt

JR = PtJ / Pt

I

Where P = nominal price of good or service as of a point in time P = Price level index at time period (t)

5. Changes in Real PricesChange in Pt

JR = (PtJR – Pt-1

JR ) / Pt-1JR

Where PtJR denotes the real price of goods (j) as of a specific period

Example 1: Nominal Prices and Changes Example 1: Nominal Prices and Changes in Price levelin Price level

Assume Year 1 is base year

Goods 1 2 3Weights 0.2 0.5 0.3

Nominal Prices Year 1: P11 =30 P2

1=100 P31=50

P L1 =0.2(30)+0.5(100)+0.3 (50)

P L1 =71

P LB= 71

Price Index P I1 =1.00


2=110 P3

2=40 PL

2 =0.2(40)+0.5(110)+0.3(40)=P L

2 =75P L

B= 71Price Index P I

2 =1.056

Example 1:Example 1: Nominal Prices and Changes in Price Level Nominal Prices and Changes in Price Level (cont’d)(cont’d)

Assume Year 1 is base year



3=108 P33=60

P L3 =0.2(35)+0.5(108)+0.3 (60)

P L3 =79


gP I2 = ((P I

2 - P I1 )/(P I

1 )) * 100=((1.056-1.00)/1.00))*100= 5.63%

gP I3 = ((P I

3 - P I2 )/(P I

2 )) * 100=((1.113-1.056)/1.056)*100= 5.33%

EXAMPLE 2:Real Prices and Changes in Real PricesReal Prices and Changes in Real Prices



1=100 P31=50

Price Index P I1 =1

Real Prices Year 1: P1R1=30/1 P2R

1=100/1 P3R1=50/1

P1R1=30 P2R

1=100 P3R1=50

----------------------------------------------------------------------------------------------------------------------------------------


2=110 P32=40


Real Prices Year 2: P1R2=40/1.056 P2R

2=110/1.056 P3R2=40/1.056

P1R2=37.87 P2R

2=104.13 P3R2=37.87

EXAMPLE 2:Real Prices and Changes in Real Prices (Cont’d)



3=108 P33=60


Real Prices Year 3: P1R3=35/1.113 P2R

3=108/1.113 P3R3=60/1.113

P1R3=31.46 P2R

3=97.06 P3R3=53.92

Changes in Real Prices Year 2 Change in PiR

2= PiR2 - PiR

1 / (PiR1) = ((37.80-30)/30)=0.26 ( (104.13-100)/100)=0.04 ((37.80-50)/50)

0.26 0.04 -0.24

Changes in Real Prices in Year 3 Change in P1R

3= P1R3 - P1R

2 / (P1R2 )= ((31.46-37.87)/37.87) ((97.06-104.13)/104.13)

((53.92-37.87)/37.87)

=- 0.17 =- 0.07 =0.42

2. NOMINAL, REAL PRICES AND INFLATION (Cont’d)

6. Inflation Adjusted Values

Pj

t+1 = Pjt ( 1 + gPt

jR ) (1 + gPIe)

Where:

Pjt+1 = denotes the estimated nominal price of good (j) in year t+1;

Pjt = denotes the nominal price of good (j) in year t ;

gPtjR = denotes the estimated growth in real price of good (j);

PIe = denotes the assumed growth in price level index from year t to year t+1

7. Constant Prices

Fixed set of prices at given year t0

Ptt+n = Pi to ; Pk

t+n =Pk to

Note: It simplifies the construction of Cash flow statements but ignores financial and economic

information that can affect the future performance of the project.

3. MARKET AND REAL EXCHANGE RATES

• The market exchange rate is the current price of foreign exchange. The market rate between the domestic currency and the foreign currency can be expressed at a point in time (t) as: E = (#D/F)t

• If the price index for the domestic currency’s economy is ID at the time t, and the price index for the foreign currency’s country is IF , then the real exchange rate (ER) at that point in time can be expressed as:

EtR = (#D/F)t * (It

F / ItD)

EtR = Et

M * (ItF / It

D) --------- EtM = Et

R * (ItD / It

F)

4. INFLATION AND NOMINAL INTEREST RATES

• Nominal Interest Rate = (i)

• Real Interest Rate = (r)

• Risk Premium = R

• Expected Growth (inflation) in Prices = gPe

• Given the factors above, nominal interest rate is• calculated as:

i = r + R + (1 + R + r) gPe

Example

• By using following information Inflation rate( gPe ) = 20%

Risk Premium ( R ) = 0

Real Interest Rate (r) = 0.05

i = r + R + (1 + R + r) gPe

i = 0.05 + 0 + (1 + 0 + 0.05)* 0.20

i = 0.26

5. IMPACTS OF INFLATION

5.1 Direct Impacts of Inflation• (i) Impact on Financial Investment

a. Costs could increase due to increases in price levels. This is normal and the model captures this. It is part of the financing plan.

b. Over-run costs are unplanned increases in costs which could be due to delay in finishing the project or unexpected increase in the cost of inputs.c. Inflation will effect the nominal value of the investment financing but it will not effect the cash flow in real values.

Table 6-1Project XYZ Financing

Period 0 1

Inflation = 0%

1. Price Index 1.00 1.00

2. Investment Outlays 500 500

Inflation = 25%

3. Price Index 1.00 1.25

4. Investment Outlays 500 625

5. Impact on Financing 0 125

6. Real Inv. Outlays (4/3) 500 500

*Inflation will not effect the real value of investment expenditure

(ii) Impact on Interest and PrincipalPayments

i = r + R + (1+R+r) gPe

At r = 5% and gPe=20% i = 26%

Comparing two cases

Case 1: $1000 loan, @ 5% Interest, No inflation

Case 2: $1000 loan, @ 5% Interest (26% in nominal rate)

In real values for both cases there is no difference in the amount of payment for interest and principal.

In real values Case 2 (inflation) pays higher installments (interest payments) and a lower principal at the end of the project compared to Case 1. Case 2 can fall into the liquidity trap during the project years, while Case 1 may not be able to pay the principal in the final year.

Table 6-2 Inflation and Its Effect on Interest and Principal Payments

Price Index1. $1000 Loan @5% Interest & No InflationLoanInterestLoan Payment

Cash Flow in Year 0 PricesNet Present Value (Equilibrium Situation)

01.0

+1000

+10000

21.0

-50

-50

11.0

-50

-50

31.0

-50

-50

41.0

-50-1000

-1050

Price Index2. $1000 Loan @ 26.0% Interest & 20% InflationLoanInterestLoan Payment

Cash Flow in Current PricesCash Flow in year 0 Prices

Net Present Value (Dis-Equilibrium Situation)3. Undiscounted Change in Cash Flow=Case 1 - Case 2 in Year 0 Prices

1.0+1000

+1000+1000

00

1.44

-260

-260-180.56

+130.56

1.2

-260

-260-216.67

+166.67

1.728

-260

-260-150.46

+100.46

2.074

-260-1000

-1260-607.64

-442.36

Period

Real Cash FlowCase 1 (No inflation) +1000 -50.00 -50.00 -50.00 -1050.00Case 2 (Inflation) +1000 -216.67 -180.50 -150.46 -607.64

(iii) Impact on Desired Cash Balances

• Inflation results in a loss in the purchasing power of the cash hold.

• When there is an inflation, sales receipts, expenditures increase in nominal prices even if the amount of goods sold does not change.

• Increase in inflation increases the desired cash balances both in nominal and real values thus the cost of the project increases.

• Inflation has an adverse effect on the outcome of the project through increasing the amount of desired cash holdings.

Inflation and Desired Cash Balances

Case A: (With Zero Inflation)

Assumptions• Zero Inflation• Desired cash = 10% of Annual Sales• Real rate of discount = 5%

0

2000

200

-200

2

2000

200

0

1

2000

200

0

3

2000

200

0

4

0

-

+200

Real PV of Holding Cash = -200 + 200/(1+.05)4 = -35.46

Year

Sales

Desired Cash

Cash Flow Impact

Inflation and Desired Cash Balances (Cont’d)

Case B: (With 20% inflation)

Assumptions• 20% Inflation• Desired cash = 10% of Sales• Real rate of discount = 5%

0

1

2000200-200-200

2

1.44

2880288-48-33

1

1.2

2400240-40-33

3

1.728

3456345.6-57.6-33

4

2.074

00

+346167

PV@ 5% = -153.66With inflation rate of 20% the cost of cash balances have increased 4.33 times

Year

Price Index

SalesDesired CashCash Flow ImpactReal Cash Flow

(iv) Impact on Accounts Receivable

• Increase in inflation will increase the sales and accounts receivable in nominal prices.

• Through inflation accounts receivables will increase in real terms as well. This will have a negative effect on the net cash flow of the project.

• Inflation has a negative effect on the outcome of the project through increasing the amount of accounts receivables in real terms.

(iv) Impact on Accounts Receivable (Cont’d)

• Likewise inflation has a positive effect on the project through accounts payable, as the payment in real values decreases.

• When inflation rises, buyers will try to postpone payments (increase accounts payable), while the sellers will try to shorten the period of payments of their customers (reduce the accounts receivables).

Impact of Inflation on Accounts Receivable and Accounts Payable

Case A: (With Zero Inflation)

Assumptions• Zero Inflation• Acts Receivable = 50% of Sales

0

2000

1000

-1000

1000

2

2000

1000

0

2000

1

2000

1000

0

2000

3

2000

1000

0

2000

4

0

0

+1000

+1000

Year

Sales

Acts Receivable

Change /AR

Receipts

Impact of Inflation on Accounts Receivable and Accounts Payable

Case B: (With 20% inflation)Assumptions• 20% Inflation• Acts Receivable = 50% of Sales

0

120001000-10001000

1000

10000

2

1.4428801440-2402640

1833

2000-167

1

1.224001200-2002200

1833

2000-167

3

1.72834561728-2883168

1833

2000-167

4

2.07400

+17281728

833

+1000-167

Year

Price IndexSalesActs ReceivableChange /ARReceiptsA. Real Receipts if 20% inflationB. Real Receipts if zero inflationDifference (A-B)

5.2 Tax Impacts of Inflation

i) Impact through Tax Deductıon of Interest Payment

• Interest payments are deducted from the taxable income, while the principal payment is not.

• As you would recall, inflation increases the interest payments in real values during the project life, while reducing the amount of principal to be paid in the final year (5.1(ii)).

• Increase in inflation has a positive effect on the outcome of the project through increasing the annual interest payment and reducing the taxable income and thus reducing the tax to be paid to the government.

Tax Impacts of InflationTax Deduction of Interest Expense

Tax shelter of interest expense because it is a deduction from taxable income

Case A: If 5% interest rate, $1000 loan, and zero inflation then

Year

Interest Expense

A: If tc = 40%, Tax savings

0 2

50

20

1

50

20

3

50

20

4

50

20

Case B: If 20% inflation, 26.0% interest, $1000 loan then:

Year

Nominal Interest Expense

Real Interest Expense

B: If tc = 40%, Tax Savings

Increased Tax Shelter (B-A)

0 2

260

180.56

72.22

52.22

1

260

216.67

86.67

66.67

3

260

150.46

60.19

40.19

4

260

125.39

50.15

30.15

(ii) Impact through Depreciation Expense and Taxes

• Depreciation allowances are deductible from the taxable income.

• When inflation rises, the depreciation allowance in real values decreases and this increases the taxable income. Thus tax payment to the government increases.

• Increase in inflation has a negative effect on the outcome of the project through reducing the depreciation allowance.

Inflation Depreciation Expense and Taxes

Investment of $1000 in year zero, depreciated over 4 years, depreciation expense is deductible from taxable income

Year

Depreciation

Tax Savings if tc = .40

A: If zero inflation, real value of tax savings

Price Index if 20% inflation

B: If 20% inflation then real value of savings

Real difference in tax savings (A-B)

0

1

2

250

100

100

1.44

69.44

30.56

1

250

100

100

1.20

83.33

16.67

3

250

100

100

1.73

57.80

42.20

4

250

100

100

2.07

48.31

51.69

(iii) Impact through Inventories and Goods Sold

• FIFO (First In First Out): Price of old inventory (input) is

used to calculate the cost of goods sold.

• LIFO (Last In First Out): Price of last input is used.

• An increases in inflation increases the amount of tax to be paid

through both approaches (FIFO and LIFO).

• In FIFO, the additional tax to be paid is spread out through the

project life.

• In LIFO, the additional tax to be paid accumulates to the final

year of the project. This is very risky.

Inflation, Inventories and Cost of Good Sold

Two ways of accounting for cost of goods sold: (1) FIFO (2) LIFO1. FIFO: If Zero Inflation

Year

A. Sales of OutputB. Purchases of InputC. COGSD. Measured Profits (A-C)E. Taxes Paid if tc = .40If 20% InflationPrice indexa. Salesb. Purchases of Inputc. COGSd. Measured Profitse. Nominal Taxes Paid if tc = .40f. If Real Taxes Paid

Difference f-E

0

0100

1.00

0100

2

30010010020080

1.44

432144120312

124.886.67

6.67

1

30010010020080

1.2

360120100260104

86.67

6.67

3

3000

10020080

1.728

518.40

144374.4

149.7686.67

6.67

Note: Additional tax liability is distributed evenly.

Inflation, Inventories and Cost of Good Sold

2. LIFO: If Zero Inflation

Year

A. Sales of OutputB. Purchases of InputC. COGSD. Measured Profits (A-C)E. Taxes Paid if tc = .40

If 20% Inflation(Price index)

a. Salesb. Purchases of Inputc. COGSd. Measured Profitse. Nominal Taxes Paid if tc = .40f. If Real Taxes Paid

Difference f-E

0

0100

1.00

0100

2

30010010020080

1.44

432144144288

115.280

0

1

30010010020080

1.2

3601201202409680

0

3

3000

10020080

1.728

518.40

100418.4

167.3696.85

16.85

Note: Additional tax liability accumulated in the final year.

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CHAPTER 6 AN INTEGRATED APPROACH TO FINANCIAL ANALYSIS